The Honduran fullback will miss the final league matches and the FA Cup final after picking up a groin injury in the 2-2 draw against Tottenham at the DW Stadium.
Figueroa was carried off on a stretcher at the DW Stadium, and he will now be unavailable for his side's crucial Premier League matches as it looks to stave off relegation, as well as the FA Cup final against Manchester City on May 11.
"We have had real negative news with Maynor Figueroa," Martinez told reporters. "He came off in the game really early and the scans have confirmed our worst fears.
"He is going to be out for the rest of the season and probably a longer period."
The news comes as a significant blow for the Latics, who have just four games left to save their top flight status, and will now have to do so without one of their most consistent performers.
The 30-year-old has only missed two games all season, with one of those coming in the Capital One Cup and the other through suspension in the league.
"He is Mr. Reliable, someone who has never missed any sort of time during the time he has been at Wigan Athletic," Martinez continued. "Unfortunately he is now going to miss the most important period in a season."
The news could also be a potential blow for the Honduran national team, which has three World Cup qualifiers next month, including one against the United States at Real Salt Lake's Rio Tinto Stadium on June 18.
Antolin Alcaraz is in the frame to replace Figueroa for Wigna after stepping up his recovery from injury, while Martinez's options are bolstered by a number of other returning absentees.
"On the other side the positive news is that Antolin Alcaraz is not too far away, but he will probably not be ready for Saturday," Martinez said. "Fraser Fyvie, Roman Golobart and Ben Watson are also stepping up and they look ready to be involved on Saturday."